FERGUSON, Mo.—Tensions flared Monday night as police confronted demonstrators here after hours of peaceful marching to protest the shooting death of an unarmed teenager by an officer.

Missouri State Highway Patrol Capt. Ron Johnson, who helps lead the security effort now in Ferguson, said at a 2 a.m. press briefing Tuesday that most peaceful protesters in the city should be applauded for their behavior. He then asked for their help...